R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: Exercise 5B

Determine $k$so that$(3k -2), (4k – 6)$ and$(k +2)$ are three consecutive terms of an $AP$.

Find the value of $x$ for which $(x+2), 2x, (2x+3)$ are three consecutive terms of an arithmetic progression.

Show that ${\left(a-b\right)}^2$ , $a^2+b^2$ and ${\left(a+b\right)}^2$are in $AP$.

Find the three numbers in $AP$ whose sum is $15$ and product is $80$.

Divide $24$ in three parts such that they are in $AP$ and their product is $440$.

Find four numbers in $AP$ whose sum is $28$ and the sum of whose squares is $216$.

Divide $32$ into four parts which are the four terms of an $AP$ such that the product of the first and fourth terms is to product of the second and the third terms as $7:15$.

The sum of first three terms of an $AP$ is $48$. If the product of first and second terms exceeds $4$ times the third term by $12$. Find the $AP$.